Common themes in Ryuk x Rem fanfiction include the discovery of new emotions. Since they are not exactly the emotional type in the original story, fanfiction writers like to explore how they would react to falling in love or developing a deep bond. Also, the theme of survival can come up. If they get involved in a situation where their lives as Shinigami are at risk, how they support each other through it can be a central theme in the stories.
One idea could be a story where Ryuk and Rem are forced to team up in the Shinigami realm to solve a mystery that threatens the balance between the human and Shinigami worlds. Another could be a fanfic exploring their relationship in an alternate universe where the rules of the Death Note world are slightly different.
In Death Note fanfiction, Ryuk and Rem have a rather complex relationship. Ryuk is more of an indifferent observer of the human world, while Rem has a deep emotional investment in Misa. Their interactions can be really interesting. Sometimes they might cross paths in the Shinigami realm or in relation to the actions of their respective human owners. Ryuk might find Rem's loyalty to Misa strange given his own non -chalant attitude towards Light. It's these differences that can create some really engaging scenarios in fanfiction.
First, you should familiarize yourself with the characters of Ryuk and Rem from the Death Note series. Know their personalities, motives, and how they interact with other characters. Then, come up with an interesting premise, like what I mentioned before. For example, a situation that brings them together in an unexpected way.
In 'Death Note Ryuk x Rem Fanfiction', a frequent theme is the contrast between their loyalties. Ryuk doesn't really have a strong loyalty to Light, he's just entertained by him. But Rem is extremely loyal to Misa. This contrast often leads to interesting scenarios where they either clash or come to some sort of understanding. Also, the theme of their different views on the power of the Death Note is common. Ryuk sees it as a source of amusement, while Rem is more cautious about its use due to her love for Misa.
One great place to start looking for Ryuk x Rem fanfiction is Archive of Our Own (AO3). There are many talented writers who create unique stories in this pairing. Some might focus on a scenario where Ryuk and Rem meet in an alternate Death Note universe. Another aspect could be how their different personalities - Ryuk's rather aloof and curious nature and Rem's loyalty and protectiveness - interact and develop a relationship in the fan - written stories.
One aspect that could be explored in such fanfictions is the idea of dependence. Light depends on Ryuk for the use of the Death Note, at least in terms of understanding its full capabilities. Ryuk, on the other hand, depends on Light for entertainment. This mutual need could be the basis for a deeper, more emotional connection in the context of yaoi fanfiction, where feelings of love or at least a strong bond could develop in unexpected ways.
Rem is very loyal. Once she decides to trust and support Subaru, she is unwavering in her commitment. For instance, she will fight alongside him without hesitation in dangerous situations.